Revision: Thermodynamics JEE Main Thermodynamics

The study of the relationships between work, temperature, heat, energy, radiation, and the physical characteristics of matter is known as thermodynamics.

The state in which two objects are at the same temperature and there is no net flow of heat between them is called thermal equilibrium.

The state of a system in which its properties do not change as long as external conditions remain unchanged is called the thermodynamic equilibrium state.

• It satisfies: mechanical equilibrium (no unbalanced forces), thermal equilibrium (no temperature differences), and chemical equilibrium (no reaction).

The temperature at which pure water freezes at 1 atm pressure is called the ice point.

When two bodies at different temperatures are brought into contact through a diathermic wall, heat flows from the hotter body to the cooler one. This continues until both reach the same temperature, at which point heat flow stops. This state is called thermal equilibrium.

A diathermic wall is a partition that freely allows heat to flow between two systems. It is shown as a thin dark line in diagrams. A thin copper sheet is a good example.

An adiabatic wall is an ideal partition that completely prevents heat transfer between two systems. In diagrams, it is shown as a thick, cross-hatched (slanting lines) region.

Thermometry is the branch of physics dealing with temperature measurement. It relies on the principle that certain physical properties of materials change continuously and predictably with temperature.

The temperature at which pure water boils and vapourises into steam at 1 atm pressure is called the steam point or boiling point.

The energy transfer due to temperature difference between a system and its surroundings is called heat.

OR

The energy that exchanges between a system and its environment because of the temperature difference between them is called heat.

• SI unit: joule (J); CGS unit: calorie

The total energy possessed by any system due to molecular motion and molecular configuration is called internal energy.

OR

The energy possessed by a system due to molecular motion and molecular configuration is called internal energy.

where U_k​ = internal kinetic energy (due to molecular motion) and U_p​ = internal potential energy (due to molecular configuration).

The energy transferred to or from a system when an external force acts on the system's boundary, causing it to move, is called work.

The thermodynamic state variables that depend on the size of the system (e.g., internal energy, volume) are called extensive variables.

The specific values of macroscopic variables that completely describe every equilibrium state of a thermodynamic system are called thermodynamic state variables.

The thermodynamic state variables that do not depend on the size of the system (e.g., pressure, temperature) are called intensive variables.

The heat capacity of a body is the quantity of heat required to raise its temperature by 1°C. It depends upon the mass and the nature of the body.

The specific heat capacity of a substance is the amount of heat energy required to raise the temperature of unit mass of that substance through 1°C (or 1 K).

OR

Heat capacity of a body when expressed for the unit mass is called the specific heat capacity of the substance of that body.

OR

The amount of heat energy required to raise the temperature of a unit mass of an object by 1 °C is called the specific heat of that object.

OR

The amount of heat per unit mass absorbed or given out by a substance to change its temperature by one unit (one degree), i.e., 1°C or 1 K, is called specific heat capacity.

OR

The quantity of heat required to raise the temperature of a unit mass of a gas by one degree, whose exact value depends upon the mode of heating the gas and can range from zero to infinity or even be negative, is called the specific heat capacity of a gas.

The quantity of heat needed to raise the temperature of the whole body by 1°C (or 1 K) is called heat capacity.

OR

The amount of heat ΔQΔQ supplied to a substance to change its temperature from T to T + ΔT, per unit mass per unit degree change in temperature, is called specific heat:

The amount of heat required to raise the temperature of one mole of a substance through a unit degree Celsius or Kelvin is called molar heat capacity.

A procedure by which the initial state of a system changes to the final state is called a thermodynamic process.

An idealised process in which at every stage the system is in equilibrium state (very slow process) is called a quasi-static process.

A process in which the temperature of the system is kept constant during the change in state (T = constant) is called an isothermal process.

OR

A thermodynamic process that takes place at constant temperature in which the internal energy of a system remains unchanged (ΔT = 0, ΔU  =0) is called an isothermal process.

A process in which there is no exchange of heat between the system and its surroundings, and the system is perfectly insulated from its environment, is called an adiabatic process.

OR

The process during which the heat content of the system or certain quantity of the matter remains constant, i.e., there is no transfer of heat between the system and its surroundings (ΔQ = 0), is called an adiabatic process.

Heat engine is a device which takes heat as input and converts this heat into work by undergoing a cyclic process.

A device that transforms heat partly into work or mechanical energy (where T_H > T_C​, Q_H > 0, Q_C < 0) is called a heat engine.

A useful state variable that measures the change in heat divided by the temperature of the system, where the combined entropy of the system and its environment remains constant if the process approaches reversibility, is called entropy.

The thermodynamic quantity that combines internal energy with the pressure-volume product, defined as H = U + PV, is called enthalpy.

A process in which the changes can be retraced in the reverse direction (e.g., melting of ice, freezing of water, condensation of steam) is called a reversible process.

A process in which the changes cannot be retraced in the reverse direction (e.g., puncturing an inflated balloon, burning a candle) is called an irreversible process.

The wall which allows the flow of heat is called a diathermic wall.

A wall of a system which does not allow the flow of heat through it is called an adiabatic wall.

Master Conversion Formula:

\[\frac{T_F-32}{180}=\frac{T_C}{100}\] = \[\frac {T_K−273.15}{100}\]

ΔU = \[\frac {3}{2}\]​nRΔT

ΔQ = ms(T₂​ − T₁​)

By substituting equation W = −p_ex . ΔV in the equation ΔU = q + W, we get

ΔU = q − p_ex . ΔV  ...(1)

If the reaction is carried out in a closed container so that the volume of the system is constant, then Δ = 0. In such a case, no work is involved.

The equation (1) becomes ΔU = q_v

Equation (1) suggests that the change in internal energy of the system is due to heat transfer. The subscript v indicates a constant volume process. As U is a state function, qv is also a state function. We see that an increase in the internal energy of a system is numerically equal to the heat absorbed by the system in a constant volume (isochoric) process.

Specific heat capacity c = \[\frac{\text{Heat capacity of body } C'}{\text{Mass of the body } m}\]

or

Specific heat capacity c = \[\frac{Q}{m\times\Delta t}\]

C = M × c = Q/(nΔT)

Unit: J/mol · K

\[Q=mc\Delta T\]

ΔS = \[\frac {ΔQ}{T}\]

If system A is in thermal equilibrium with system C, and system B is also in thermal equilibrium with system C, then systems A and B are in thermal equilibrium with each other.

By substituting equation W = −p_ex . ΔV in the equation ΔU = q + W, we get

ΔU = q − p_ex . ΔV  ...(1)

If the reaction is carried out in a closed container so that the volume of the system is constant, then Δ = 0. In such a case, no work is involved.

The equation (1) becomes ΔU = q_v

Equation (1) suggests that the change in internal energy of the system is due to heat transfer. The subscript v indicates a constant volume process. As U is a state function, qv is also a state function. We see that an increase in the internal energy of a system is numerically equal to the heat absorbed by the system in a constant volume (isochoric) process.

Statement:
The net heat energy supplied to a system is equal to the sum of the change in internal energy of the system and the work done by the system. It is based on the law of conservation of energy.

Formula:

where Q = heat added, ΔU = change in internal energy, W = work done by the system.

The second law of thermodynamics states that the total entropy of a system and its surroundings increases in a spontaneous process.

Mathematically,

ΔS_total = `Delta S_"system" + Delta S_"surroundings" gt 0`

For an equilibrium:

ΔS_total = 0

Kelvin-Planck Statement: It is not feasible for any heat engine to utilise all the heat it receives from a source and convert it entirely into useful work. In other words, achieving 100% efficiency in converting heat into work is impossible.

Clausius Statement: Without any external assistance, a machine cannot transfer heat from a colder reservoir to a hotter one. In essence, heat cannot spontaneously move from a cooler object to a warmer one without external intervention or work being done.

• Isothermal → P-V diagram: Hyperbolic curve (inverse relation); T-V: horizontal line; T-P: vertical line.
• Adiabatic → P-V diagram: Steeper curve than isothermal; T-V: exponential decay/growth; P-T: exponential decay/growth.
• Work done = area under the P-V curve.
• Adiabatic curve is steeper because γ > 1 (slope = −γP/V vs −P/V for isothermal).

First Law: Energy of system + surroundings remains constant → ΔU = q + W

ΔU: change in internal energy, q: heat, W: work done on system

Sign convention:

• Work by system (−)
• on system (+)
• Heat absorbed (+)
• released (−)

ΔU > 0: energy enters system; ΔU < 0: energy leaves system

• Isothermal: ΔU = 0 → q = −W
• Adiabatic: q = 0 → ΔU = W
• Isochoric: W = 0 → ΔU = q
• Isobaric: ΔU = q + W

• Heat energy absorbed (Q) depends on: mass (m), rise in temperature (Δt), and specific heat capacity (c), i.e., Q ∝ m × Δt × c.
• Heat capacity (C') and specific heat capacity (c) are related by: C′ = m × c.

Entropy (S): A thermodynamic property that measures the degree of randomness or disorder of a system.

\[\Delta S=\frac{q_{rev}}{T}\]

Second Law: The entropy of the universe always tends to increase during any spontaneous process.

Total entropy change:

Entropy of mixing:

(ΔS for mixing is always positive, since ΔS is always fractional/positive)

• The Second Law states that there exists a useful state variable called entropy S.
• If a system's change in entropy ΔS = ΔQ/T, the combined entropy of the system and environment remains constant if the process is reversible.
• The Second Law shows: if a physical process is irreversible, the combined entropy of the system and environment increases.
• Final entropy must be greater than initial entropy for an irreversible process: S_f > S_i
• For any process approaching reversibility: ΔS_total ≥ 0
• For an isolated system: ΔU_system ≥ 0 and ΔS_total ≥ 0
• The Second Law is also known as the Law of Increased Entropy.
• No process is possible whose sole result is the absorption of heat from a reservoir and conversion of that heat entirely into work (Kelvin-Planck statement).